Question

If the length of arc ST is 3 pi and RS = 12, calculate angle TRS. *Round your answer to the nearest hundredth.

Answer 1

Consider the angle formed by the lines RS and RT. This is the angle that we want find. In general, for a circle, the arc formed by two lines that start at the center of the circle has a lenght that is related to the angle (in radians) formed by the lines and the radius of the circle by the following formula.

`S\text{ = r }\theta`

where S is the arc lenght. In our case, we have

`3\pi\text{ = r }\theta`

In this case, r is the radius of the circle, which is known to be the lenght of the line RS, which is 12.

So, we get the equation

`3\pi=12\theta`

If we divide on both sides by 12, we get

`(3\pi)/(12)=\theta=(\pi)/(4)`

so the angle is pi/4.. By using an approximation for the value of pi (3.1416) so you can find a value of theta of 0.785 radians, which rounded to the neares hundredth is 0.79 radians